Thanks for the replys guys, I have done some research into some cornish palm trees. If I knew how to add pics I could show you all the angles I will check the soil aswell, also its abit boggy at the back so could do with sorting out somehow, maybe a tree to soak up some water. Also would like some aggregate to brighten it up.

It's not a massive garden its long and thin, as for the sun, it goes from left to right throughout the day, at the moment it goes behind the house around 1.30pm ish but the back of the garden gets sun all of the day. Thanks again guys will try to sort out pics soon.